I am a Hanafi female who often has much discharge including while performing prayers. In such a situation, can I continue to complete the prayers or do I have to cleanse and pray again?
Your prayer is valid and you do not need to pray again. Cleaning the area of the discharge is good but it is not a condition for validity of you Prayer. This is when the discharge is not blood. If it was blood which came out and made pats of your outer body Najis, then you need to wash and clean it.
Wassalam.